Satellite constellation for measuring atmospheric wind speeds using doppler lidar

ABSTRACT

A constellation of satellites comprising at least two satellites in the same orbit is used to measure atmospheric wind speeds by means of a spatial wind lidar; each satellite carries a Doppler lidar, with a fixed sight axis. The orbit is a polar or quasi-polar orbit, with an orbital altitude from 350 to 500 km. The sight angles and the distribution of the satellites in the orbit are chosen so that the tracks on the surface of the Earth of the sight axes of the satellites of the constellation are substantially coincident over half of the surface of the Earth and regularly distributed over the other half of the surface of the Earth.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is based on French Patent Application No. 00 10190 filed Aug. 2, 2000, the disclosure of which is hereby incorporatedby reference thereto in its entirety, and the priority of which ishereby claimed under 35 U.S.C. §119.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention relates to measuring atmospheric wind speeds usingspatial wind lidar. The atmospheric wind speed is a fundamentalcomponent of operational meteorology; it is therefore of direct interestto scientists and to many commercial companies.

[0004] 2. Description of the Prior Art

[0005] Obtaining terrestrial global measurements is no longer compatiblewith existing ground and airborne systems, which cover only a limitedfraction of the terrestrial surface (oceanic areas in particular arevery badly covered); it has therefore been proposed to carry outmeasurements from space, using Doppler lidar, to obtain sufficientmeshing of measurements to satisfy the requirements stated bymeteorologists, in particular of Eumetsat and Météo-France.

[0006] The principle of lidar (also known as optical radar) is analogousto that of radar: an optical wave emitted by a laser emitter isback-scattered by molecules and particles in the atmosphere to areceiver which is located, in the case of spatial lidar, near the laseremitter; the received signal is then fed to a detector and processorsystem and then transmitted to the ground for possible additionalprocessing. The return signal is sampled in time to obtain informationcorresponding to each atmosphere layer through which it has passed: thelidar is therefore inherently a sounder. In the case of Doppler lidar,the processing of the signal entails using means that depend on the typeof detection employed (direct, coherent, heterodyne, etc) to determinethe frequency difference between the wavelength emitted by the laser andthat of the return signal, which yields directly the projection onto thesight axis of the speed difference between the carrier of the emitterand the molecules and/or particles that back-scattered the laser signal;appropriate algorithms deduce from the speed difference information onthe components of the speed of the wind in the sounded area: ideally,measurements along three different sight axes at a given point yield thethree components of the wind vector at that point (two in the horizontalplane and the third along a vertical at the location concerned). Thevertical speed of the wind can also be ignored, two measurements at eachpoint being considered sufficient.

[0007] U.S. Pat. No. 5,367,371 describes the principle of atmosphericwind speed measurement by spatial lidar, as explained above. It suggestsproviding a satellite with two telescopes with sight angles of 45° tothe roll axis of the satellite. With regard to orbits, the documentlimits itself to describing the locations of the points of impact of therays of the two telescopes for a given orbit of the satellite. Theproblem of terrestrial coverage is mentioned, but in point of factmerely in terms of it being a requirement, with no real solution beingprovided.

[0008] U.S. Pat. No. 5,872,621 concerns a solution to the problem ofreception in spatial lidar; it proposes to use a holographic opticalmember to direct the back-scattered beam toward the receiver of thelidar. The holographic optical member is driven in rotation to scan thearea to be covered. As in the previous document, this document refers tothe coverage problem only to show the cycloid curve formed by the locusof the points of impact of the beam on the ground for a given trajectoryof the satellite.

[0009] Additionally, various satellite observation methods based on theDoppler effect have been proposed. JP-A-10 19683 proposes, in aconstellation of at least three satellites, sending laser pulses fromone satellite to a mirror on other satellites rotating in oppositedirections. The pulses are reflected toward the source satellite and thetime difference between the pulses is measured; a measured value of theelectromagnetic ether speed is deduced from this. U.S. Pat. No.4,463,357 proposes to measure the electron content of the ionospherebetween a spacecraft and a receiver by crossed correlation of twocoherently modulated signals; using GPS satellites and a plurality ofground stations, it is possible to locate terrestrial events that giverise to ionospheric disturbances—such as volcanic eruptions or thelaunch of intercontinental missiles. U.S. Pat. No. 5,428,358 proposes ananalogous way to measure the electron content of the ionosphere usingsatellites of the GPS constellation. U.S. Pat. No. 5,675,081 proposes asystem for measuring the water content of the atmosphere using watervapor radiometers and the satellites of the GPS constellation. The abovedocuments are silent on the subject of measuring atmospheric windspeeds; nor do they mention the problem of determining orbits for suchmeasurements.

[0010] Thus measuring atmospheric wind speeds gives rise to variousproblems. A first major problem lies in the weakness of the resourcesavailable on board a satellite (mainly in terms of electrical power),compared to those available on the ground, given the very severe demandsof scientists both as to the accuracy of the wind speed measurement andthe number of sight axes. A second problem is that of the geographicalcoverage of the measurements: a spatial system for measuring wind speedsusing lidar mounted on a constellation of satellites would be of greaterinterest if it were able to provide:

[0011] the widest possible coverage of the terrestrial surface, and

[0012] the greatest number of measurements for each individual cellsounded, using different sight axes; a cell typically has the followingdimensions: 200×200 km horizontally, with a vertical dimension of a fewhundreds of meters, typically from 500 m to 1 km.

[0013] The invention proposes a solution to the various problems justmentioned. First of all, it uses a limited number of very simplemeasuring satellites. A preferred embodiment of the invention providesgood terrestrial coverage. In a first configuration, the measurementpoints are distributed substantially regularly over half of the surfaceof the terrestrial globe, i.e. the sight axes of the instruments mountedon the various satellites are projected onto the ground at points which,combined with each other, constitute trajectories (referred to astracks) whose intersections with the equator are quasi-equidistant. In asecond configuration, over the other half of the surface of theterrestrial globe, the measurement points are grouped by areas(typically with dimensions less than 200×200 km), i.e. the sight axes ofthe instruments mounted on the various satellites are projected onto theground at points contained within said areas. The two configurations areeach produced over a period of 12 hours, at intervals of 24 hours, andthe halves of the surface of the globe referred to vary in time at arate that can be chosen by varying the altitude of the satellites. Thisembodiment of the invention therefore yields measurements that are easyfor meteorologists to use.

SUMMARY OF THE INVENTION

[0014] The invention proposes a constellation of satellites formeasuring atmospheric wind speeds, the constellation including at leasttwo satellites distributed over the same non-geosynchronous orbit andeach carrying a Doppler lidar.

[0015] The sight axis of the Doppler lidar of a satellite is preferablyfixed. In one embodiment of the invention the orbit is a polar orquasi-polar orbit. It is also advantageous if the orbital altitude isfrom 350 km to 500 km.

[0016] In one embodiment the constellation includes three satellites andthe orbital altitude is from 400 km to 500 km.

[0017] It is also advantageous if the sight angle of one satelliterelative to the nadir is from 30° to 50° and is preferably about 45°.

[0018] In another embodiment the satellites of the constellation havedifferent angles between the projection of the sight axis on the surfaceof the Earth and the projection of the speed of the satellite on theEarth.

[0019] In this case the constellation can include two satellites and thedifference between the angles is then from 75° to 105° and is preferablyabout 90°.

[0020] The constellation can also include three satellites and in thiscase the difference between the angles is from 90° to 150° and ispreferably about 120°.

[0021] The tracks on the surface of the Earth of the sight axes of thesatellites of the constellation are advantageously substantiallycoincident in a first area of the surface of the Earth. The tracks onthe surface of the Earth of the sight axes of the satellites of theconstellation can also be substantially regularly distributed in asecond area of the surface of the Earth.

[0022] In one embodiment the constellation satisfies the condition:${\frac{2\pi \quad T_{S}}{nT}R} < {{\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}} - {\tan \quad \alpha_{i}\sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}}} \leq {a + {\frac{2\quad \pi \quad T_{S}}{nT}R}}$

[0023] in which n is the number of satellites in the constellation, T isthe period of rotation of the Earth, T_(S) is the orbital period, R isthe radius of the Earth, H is the orbital altitude, γ is the anglebetween the projection of the speed of satellite t on the surface of theEarth on passing over the equator and the rotation speed of the earth atthe equator, α_(i) is the angle between the sight axis of satellite iand the nadir, (Pi is the angle between the projection on the Earth ofthe sight axis of satellite i and the projection on the Earth of thespeed of that satellite, ψ_(i,i+1) is the angle measured in the plane ofthe orbit between the satellites i and i+1, and a is a parameteranalogous to a distance and is less than 500 km.

[0024] In this case it is advantageous if the parameter a has a valueless than 100 km and preferably less than 50 km.

[0025] In another embodiment the angle between two satellites of theconstellation in the plane of the orbit satisfies the condition:${\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} \leq {\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i}\sin \quad \phi_{i}} - {\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}}}}} \leq {{\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} + b}$

[0026] in which T is the rotation period of the Earth, T_(S) is theorbital period, H is the orbital altitude, γ is the angle between theprojection of the speed of satellite i on the surface of the Earth oncrossing the equator and the rotation speed of the Earth at the equator,α_(i) is the angle between the sight axis of satellite i and the nadir,φ_(i) is the angle between the projection of the sight axis of satellitei on the Earth and the projection of the speed of the satellite on theEarth, ψ_(i,i+1) is the angle measured in the plane of the orbit betweensatellites i and i+1, and b is a parameter analogous to a distance andis less than 200 km.

[0027] In this case the parameter b has a value less than 20 km andpreferably less than 10 km.

[0028] Other features and advantages of the invention will becomeapparent on reading the following description of embodiments of theinvention, which description is given by way of example and withreference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0029]FIG. 1 is a schematic representation of a system of axes used fora satellite.

[0030]FIG. 2 is a schematic representation of a constellation ofsatellites.

[0031]FIG. 3 is a diagrammatic representation of a constellation of twosatellites in a first embodiment of the invention.

[0032]FIG. 4 is a diagrammatic representation of the sight angle of thefirst satellite from the constellation shown in FIG. 3.

[0033]FIG. 5 is a diagrammatic representation of the sight angle of thesecond satellite from the constellation shown in FIG. 3.

[0034]FIG. 6 shows the intersections of the sight axes with the surfaceof the globe for the constellation shown in FIG. 3.

[0035] FIGS. 7 to 9 are similar to FIGS. 4 to 6 for anotherconstellation in accordance with the invention comprising twosatellites.

[0036] FIGS. 10 to 14 are similar to FIGS. 3 to 6 for a constellation inaccordance with the invention comprising three satellites.

[0037] FIGS. 15 to 18 are similar to FIGS. 11 to 14 for anotherconstellation in accordance with the invention comprising threesatellites.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] The invention proposes to use a constellation of satellites eachhaving a sight axis (or firing line) that is preferably fixed to measureatmospheric winds by Doppler lidar. The satellites are distributedaround the some orbit, to provide good terrestrial coverage. Theinvention therefore enables the structure of the satellite to besimplified without compromising the results obtained. Possible satellitepositions and firing angles are explained in detail in the remainder ofthe description.

[0039]FIGS. 1 and 2 show the conventions used hereinafter to explain theinvention. FIG. 1 is a diagrammatic representation of a system of axesused for a satellite; the system of axes is a direct orthonomic systemof axes. The axis z passes through the center of the Earth and thesatellite. The axis x is parallel to the projection of the speed of thesatellite onto the surface of the Earth; the axis y is perpendicular tothe previous two axes. For the satellite i, φ_(i) denotes the azimuth ofthe laser sight axis relative to the projection of the speed of thesatellite on the ground, in other words the angle between the axis x andthe projection of the sight axis on the ground; the sign of this angleis determined by the direction of the system of axes, the angle beingpositive when the projection is in the first quadrant, between the axesx and y, as shown in the figure. For the satellite i, α_(i) denotes theangle between the sight axis and the nadir, in other words the anglebetween the axis z and the sight axis. FIG. 2 is a diagrammaticrepresentation in the plane of their orbit, which is a polar orbit inthis example, of a constellation of two satellites i and i+1; byconvention, the satellite i is ahead of the satellite i+1 in the orbitalarc, in the direction in which they travel around the orbit. Therelative angular phase of the two consecutive satellites i and i+1 isdenoted ψ_(i,i+1).

[0040] Possible characteristics of a constellation in accordance withthe invention are described next. The constellation comprises at leasttwo satellites; the examples shown in FIGS. 3 to 9 are of constellationswith two satellites, which provide satisfactory results, and whichenable measurement of two components of wind speeds, typicallyhorizontal wind speeds. Constellations of three satellites can also beused, as in the examples shown in FIGS. 10 to 18. Constellations ofthree satellites enable three components of wind speed to be measured,and therefore horizontal and vertical speeds. The invention applies to aconstellation reduced to two or three satellites, as in these examples;it can easily be generalized to n satellites (n>3), although aconstellation with more than three satellites is of only limitedbenefit, for the following reasons:

[0041] three measurements along different sight axes are sufficient todetermine the wind vector in three dimensions, and

[0042] the cost of a system with n>3 satellites would run the risks ofbecoming prohibitive.

[0043] The orbit of the satellites in the constellation isadvantageously a polar or quasi-polar orbit; a quasi-polar orbit is anorbit whose inclination is from approximately 80° to approximately 100°;one example of a quasi-polar orbit is a heliosynchronous orbit, whichenables the satellite to overfly the Earth under similar conditions ofillumination from one orbit to another. A heliosynchronous orbit isparticularly suitable for the mission described, in that it ensures goodcoverage of the whole of the terrestrial surface; the invention can alsobe applied to other types of orbit, such as highly inclined orbits; suchorbits enable tropical areas to be overflown more frequently than apolar or quasi-polar orbit, but provide no or only poor coverage ofnorthern areas.

[0044] The orbital altitude H of the satellites of the constellation istypically from 350 km to 500 km; in the case of a constellation withthree satellites, it is advantageous for the altitude to be from 400 kmto 500 km. That range of altitudes satisfies two constraints; firstly,the accuracy of the wind speed measured by lidar depends on themagnitude of the back-scattered signal: low altitudes, i.e. altitudesbelow 500 km, are therefore preferred, since the intensity of theback-scattered signal is inversely proportional to the distance betweenthe transmitter and the back-scattering target. On the other hand, thelower the orbital altitude, the shorter the service life of thesatellite, because of atmospheric braking, unless the satellite carriesmore fuel, which commensurately increases the mass and the volume of thesatellite. It is advantageous to choose altitudes greater than 350 km.

[0045] The orbital period T_(S) is then deduced from the chosenaltitude; it is of the order of 90 to 100 minutes for orbital altitudesfrom 350 km to 500 km, and is given by the equation:$T_{S} \approx {2\pi \quad \sqrt{\frac{\left( {R + H} \right)^{3}}{\mu}}}$

[0046] in which μ is the terrestrial gravitational constant, equal toapproximately 4×10⁵ km³/s², R is the radius of the Earth (approximately6 400 km) and H is the orbital altitude.

[0047] The distribution of the satellites in the orbit is advantageouslya function of the sight axis chosen for each satellite, discussed next.The sight angle of the laser relative to the nadir for a satellite ispreferably from 30° to 50°, and is typically around 45°, as in theexamples given below. In the FIG. 1 system of axes, this angle ismeasured between the axis z and the sight axis—it being understood thatthe satellite is sighting toward the surface of the Earth. The lowerlimit of this range minimizes the error produced into the calculatedhorizontal component of the wind by the vertical speed of the wind,especially in a configuration with two satellites; at the limit, anangle of 90° would be the optimum, but the laser would no longer befiring into the atmosphere. The upper value of the range is a responseto the constraints of minimizing the thickness of the atmosphere passedthrough and maximizing the back-scattered signal: the greater the angle,the greater the quantity of air passed through, and the weaker thesignal back-scattered by the masses of air in motion.

[0048] In the preferred embodiment, the invention proposes to choose thesight axis of each satellite and the distribution of the satellites ofthe constellation so as to define two areas of the surface of the Earth.In a first area, the tracks on the surface of the Earth of the sightaxes of the satellites of the constellation are substantiallycoincident; in other words, in that area, a point on the surface of theEarth reached by the sight axis of a first satellite of theconstellation is then reached by the sight axis of the other satellitesof the constellation. The accuracy in this case is that required bymeteorologists. For wind speed measuring applications, it is typicallybeneficial to know the speed in areas 200 km by 200 km. In the contextof this description, the tracks are considered to be coincident orsubstantially coincident if the distance between the tracks is less than200 km, or even less than 100 km. In this first area, the invention canmeasure wind speeds horizontally (in the case of a constellation withtwo satellites) or horizontally and vertically (in the case of threesatellites). The speed of the wind can therefore be determined at eachof the points sighted.

[0049] In a second area, the measurement points are distributed in asubstantially regular manner; in other words, the intersections with thesurface of the Earth of the sight axes of the various satellites of theconstellation constitute trajectories or tracks. The intersections ofthese tracks with the equator are quasi-equidistant. In this areaone-dimension information on the wind is therefore obtained, i.e. theprojection of the wind along the sight axis for each measurement, at asmany locations on the Earth as there are measurement points; morenumerous measurement points are obtained in this area than in the firstarea, as shown in the figures.

[0050] Each of the two areas advantageously corresponds to half thesurface of the Earth. Also, by optimizing the orbital characteristics:

[0051] the two configurations are each produced over a period of 12hours, at intervals of 24 hours, and

[0052] the areas mentioned vary in time at a rate that can be chosen byvarying the altitude of the satellites.

[0053] Thus for a given point on the surface of the Earth, and over aperiod of 24 hours, it is possible to obtain a measurement of the windspeed with two or three components and a measurement of the wind speedin a single direction. The invention lends itself particularly well tometeorological applications, with one measurement and one update orconfirmation of the measurement every 24 hours. As the examples show,there are terrestrial areas, located toward latitudes of the order of±50° (with two satellites) or ±20° (with two satellites), in which, in12 hours and over one half of the terrestrial surface, the sight axeswill reach substantially the same cells, with the benefit of a morehomogeneous coverage over the other half of the terrestrial surface, inwhich the cells will be addressed by only one sight axis.

[0054] The invention has the unique advantage of combining, with thesame constellation of satellites, measurements distributed substantiallyregularly over the surface of the terrestrial globe and measurementsthat are distributed less uniformly but are concentrated in certaincells: the areas addressed by several sight axes over a time periodequivalent to a fraction of an orbit (typically a few tens of minutes)provide wind measurements that are more directly usable, throughreducing recourse to assimilation models; in particular, for thesituation with three sight axes, the three components of the speed ofthe wind at the measurement point are obtained in the cells of the firstarea. The invention therefore enables the calibration of the models tobe improved if, in these cells, the measurement of the wind speed can beobtained by other in situ means, for example balloons.

[0055] The invention also makes it possible to shift the sighted areasby varying the orbital altitude. The rate at which the areas are shiftedcan be from a few days to a few weeks, depending on user requirements;measurements can therefore be carried out at different places.

[0056] The position of the satellites of the constellation in the orbitand the sight axes can be determined in the following manner. To obtaina regular distribution of the tracks of the satellites in the secondarea, the following condition is advantageously applied: $\begin{matrix}{{\frac{2\pi \quad T_{S}}{nT}R} < {{\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}} - {\tan \quad \alpha_{i}\sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}}} \leq {a + {\frac{2\quad \pi \quad T_{S}}{nT}R}}} & \lbrack 1\rbrack\end{matrix}$

[0057] for i varying from 1 to n−1, where n is the number of satellitesin the constellation. In the above equation, T_(S), R, H, α_(i), φ_(i),ψ_(i,i+1) have the meaning referred to above. T is the period ofrotation of the Earth, that is to say approximately 86 200 s and γ isthe angle between the projection of the speed of the satellite i on thesurface of the Earth on passing over the equator and the rotation speedof the Earth at the equator; in the example considered here of a polarorbit:${\tan \quad \gamma} \approx {\frac{2\pi \quad R}{T}\sqrt{\frac{R + H}{\mu}}}$

[0058] In equation [1], the parameter a is an error term, typically of afew hundred kilometers, for example less than 500 km; the farther fromzero the value of a, the less equidistant are the intersections of thetracks of the trajectories with the equator; consequently, ideally: a=0,in other words: $\begin{matrix}{{{\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}} - {\tan \quad \alpha_{i}\sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}}} = {\frac{2\pi \quad T_{S}}{nT}R}} & \left\lbrack 1^{\prime} \right\rbrack\end{matrix}$

[0059] The above condition ensures a regular distribution of thetrajectories in the second area, in other words good scanning of thesurface of the Earth in the second area.

[0060] The following constraint can be imposed to ensure grouping of thetracks of the satellites in the first area: $\begin{matrix}{{\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} \leq {\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i}\sin \quad \phi_{i}} - {\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}}}}} \leq {{\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} + b}} & \lbrack 2\rbrack\end{matrix}$

[0061] in which the various parameters have the same meaning and b is anerror term, typically of a few tens of kilometers, generally less than200 km. The farther from zero the value of b, the farther apart are theprojections of the sight axes on the ground; consequently, ideally: b=0,in other words: $\begin{matrix}{{\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}} - {\tan \quad \alpha_{i}\sin \quad \phi_{i}}}}} = {\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}}} & \left\lbrack 2^{\prime} \right\rbrack\end{matrix}$

[0062] The above condition ensures good overlapping of the tracks in thefirst area. Values of b less than 20 km, or even less than 10 km, can bechosen, as in the configurations with three satellites referred to aboveby way of example.

[0063] In the preferred embodiment of the invention the parameters a andb have zero values and ψ_(i,i+1)=π/n, in other words an angle betweensatellites of 90° is chosen for a constellation of two satellites andangle between satellites of 60° is chosen for a constellation of threesatellites; under these conditions, in the simplified particular casewhere α_(i)=α_(i+1) (=β), given the orders of magnitude of the variousparameters, the following results are obtained.

[0064] For a constellation of two satellites, compliance with equations[1′] and [2′] imposes that φ_(i) and φ_(i−1) be of opposite sign; if itis additionally assumed (this is not a restricting condition) thatφ₁=−φ₂ (=φ, positive), the following equation is obtained:${\tan \quad {\alpha sin}\quad \phi} = {\frac{\pi}{4}\cos \quad \gamma \quad \frac{T_{S}R}{TH}}$

[0065] that varies between approximately 0.92 for H=350 km andapproximately 0.66 for H=500 km.

[0066] For values of the angle α of 45°, possible values for the angle φare therefore of the order of 66° for an altitude of 350 km and of theorder of 41° for an altitude of 500 km.

[0067] In a constellation with three satellites the above conditions arewritten, for zero values of a and b:${\tan \quad {\alpha \left( {{\sin \quad \phi_{2}} - {\sin \quad \phi_{1}}} \right)}} = {{\tan \quad {\alpha \left( {{\sin \quad \phi_{3}} - {\sin \quad \phi_{2}}} \right)}} = {\frac{\pi}{3}\cos \quad \gamma \frac{T_{S}R}{TH}}}$

[0068] this quantity varying from approximately 1.22 for H=350 km toapproximately 0.88 for H=500 km.

[0069] For H=500 km, one possible solution is φ₂=0 and φ₁=−φ₃ (=φ,positive); for a value of a of 30°, a value of φ is obtained of theorder 50°, and for a value of a of 45°, a value of φ of the order 62°.In the case of a configuration with three satellites, equations [1′] and[2′] can be satisfied only by values of the altitude H satisfying thecondition:$\frac{H}{\sqrt{\left( {R + H} \right)^{3}}\cos \quad \left( {{Arctan}\quad \frac{2\pi}{R}\sqrt{\frac{R + H}{µ}}} \right)} > {\frac{2\quad \pi^{2}}{3}\frac{R}{T\sqrt{µ}}}$

[0070] in other words, approximately, H>435 km.

[0071] Solutions can of course be found for lower altitude values, inparticular with values of the angle α that are different for thesatellites of the constellation, or for nonzero values of the parametersa and b.

[0072] The equations given above are for a flat Earth approximation. Theerror induced by this approximation is of the order of a few percent(for H=500 km and α=45° the error is approximately 4%), and theequations therefore remain applicable.

[0073] If the flat Earth approximation is not used, the above equations[1], [1′], [2] and [2′] are modified by replacing Htanα with:$R\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha} \right)} - \alpha} \right\rbrack$

Equation  [1]  then  becomes  equation  [1₀]:${{\frac{2\pi \quad T_{S}}{n\quad T}R} < U \leq {a + {\frac{2\pi \quad T_{S}}{n\quad T}R\quad {with}U}}} = {{\frac{R}{\cos \quad \gamma}{{{\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i + 1}} \right)} - \alpha_{i + 1}} \right\rbrack \sin \quad \phi_{i + 1}} - {{R\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i}} \right)} - \alpha_{i}} \right\rbrack}\sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{j + 1}}}}$

[0074] for i=1 to n−1.${{{Equation}\quad\left\lbrack 1^{\prime} \right\rbrack}\quad {becomes}\quad {{equation}\quad\left\lbrack 1_{0}^{\prime} \right\rbrack}\text{:}}\frac{R}{\cos \quad \gamma}{{{{\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i + 1}} \right)} - \alpha_{i + 1}} \right\rbrack \sin \quad \phi_{i + 1}} - {\quad{\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i}} \right)} - \alpha_{i}} \right\rbrack \quad \sin \quad \phi_{i}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{j + 1}}}} = {\frac{2\quad \pi \quad T_{S}}{n\quad T}R}}}$

Equation  [2]  becomes  equation  [2₀]:${\frac{T_{S}}{T}R\quad \psi_{i,{j + 1}}} \leq V \leq {{\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} + {b\quad {with}}}$$V = {\frac{R}{\cos \quad \gamma}{\left\lbrack {{Arcsin}\quad {\quad{{\left. {\left. \left( {\quad{\frac{R + H}{R}\sin \quad \alpha_{i}}} \right. \right) - \quad \alpha_{i}} \right\rbrack \quad \sin \quad {\quad{\phi_{i} - \quad \quad {\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i + 1}} \right)} - \alpha_{i + 1}} \right\rbrack \quad \sin \quad \phi_{i + 1}}}}}}\quad}} \right.}}$

[0075] for i=1 to n−1.Equation  [2^(′)]  becomes  equation  [2₀^(′)]:${R{{{\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i + 1}} \right)} - \alpha_{i + 1}} \right\rbrack \sin \quad \phi_{i + 1}} - \quad \quad {\left\lbrack {{{Arcsin}\left( {\frac{R + H}{R}\sin \quad \alpha_{i}} \right)} - \alpha_{i}} \right\rbrack \quad \sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{j + 1}}}$

[0076] For three satellites, equations [1₀′] and [2₀′] can be satisfiedonly for H>418 km if the roundness of the Earth is taken into account(compared to 435 km if the Earth is considered flat). Note that theresults set out in the remainder of the description with reference toFIGS. 3 to 18 were obtained from a simulation taking the roundness ofthe Earth into account.

[0077] Embodiments of the invention are described next with reference toFIGS. 3 to 18. FIG. 3 is a diagrammatic representation of aconstellation of two satellites in a first embodiment of the invention;it shows the two satellites in the plane of their orbit, which is apolar orbit. The satellites are offset by ψ_(1,2)=120° in the orbit.FIG. 4 is a diagrammatic representation of the sight angle of the firstsatellite of the constellation from FIG. 3; the value of the angle α is45° and the first satellite sights on the right-hand side, i.e. with anangle φ₁ of −90°. FIG. 5 is a diagrammatic representation of the sightangle of the second satellite of the constellation from FIG. 3; thevalue of the angle α is again 45°, and the angle φ₂ is zero. In thisconfiguration, the respective values of the parameters a and b are 60 kmand 400 km.

[0078]FIG. 6 is a representation of the intersections of the sight axeswith the surface of the globe for the FIG. 3 constellation; the track ofthe first satellite is shown by squares and the track of the secondsatellite is shown by crosses. The first area and the second area, whichare indicated at the bottom of the diagram, can clearly be distinguishedin this figure.

[0079] FIGS. 7 to 9 are representations similar to FIGS. 4 to 6 foranother constellation in accordance with the invention with twosatellites; in this constellation, the position of the two satellites inthe orbit is the same as in FIG. 3. FIG. 7 shows the sight angle of thefirst satellite, with respective values of the angles α and φ₁ of 45°and 0°. FIG. 8 shows the sight angle of the first satellite, withrespective values of the angles α and φ₂ of 45° and −90°. FIG. 9 showsthe track of the satellites on the surface of the Earth. In thisconfiguration the respective values of the parameters a and b are 60 kmand 400 km, as in the preceding configuration. Although these values arenot zero, the figures show that the measurement points are distributedin two areas, as proposed by the invention.

[0080] FIGS. 10 to 18 show similar views for a configuration with threesatellites. FIG. 10 shows the three satellites in the plane of theirpolar orbit. The satellites are offset by ψ_(1,2)=ψ_(2,3)=60° in theorbit. FIG. 11 is a diagrammatic representation of the sight angle ofthe first satellite of the constellation from FIG. 10; the value of theangle α is 45° and the first satellite sights to the rear left-handside, with an angle φ₁ of 120°. FIG. 12 is a diagrammatic representationof the sight angle of the second satellite of the constellation; thevalue of the angle α is again 45° and the angle φ₂ is zero. FIG. 13 is adiagrammatic representation of the sight angle of the third satellite ofthe constellation; the value of the angle α is again 45° and the valueof the angle φ₃ is −120°. FIG. 14 shows the tracks of the threesatellites on the surface of the Earth; the two areas can again be seenclearly. In this configuration, the value of each of the parameters aand b is 10 km.

[0081] FIGS. 15 to 18 are similar to FIGS. 10 to 14 for anotherconstellation with three satellites. Like that of FIGS. 10 to 14, theconstellation comprises three satellites in a polar orbit; the positionof the three satellites in their orbit is similar to that of FIG. 10.FIGS. 15 to 18 show the sight angles of the three satellites; in allcases the value of the angle α is 45° and the values of the angles φ₁,φ₂ and φ₃ are respectively −60°, 180° and 60°. FIG. 18 shows the tracksof the satellites, with the same conventions as FIG. 14. The three areascan clearly be recognized again. In this example the value of both theparameters a and b is 10 km.

[0082] The examples show that the invention can usefully be employedeven with nonzero values of the parameters a and b.

[0083] Of course, the present invention is not limited to the examplesand embodiments described and shown, many variants of which will suggestthemselves to the skilled person. The various conditions set out abovecan advantageously be combined, but it is also possible for only some ofthem to be used; only the conditions [1] or [1′] could be used, withoutusing the conditions [2] or [2′], if the required objective were toobtain a distribution in one area but not to obtain a grouping in theother area.

There is claimed:
 1. A constellation of satellites for measuringatmospheric wind speeds, said constellation including at least twosatellites distributed over the same non-geosynchronous orbit and eachcarrying a Doppler lidar.
 2. The constellation claimed in claim 1wherein the sight axis of said Doppler lidar of a satellite is fixed. 3.The constellation claimed in claim 1 wherein said orbit is a polar orquasi-polar orbit.
 4. The constellation claimed in claim 1 wherein theorbital altitude is from 350 km to 500 km.
 5. The constellation claimedin claim 4 including three satellites and in which the orbital altitudeis from 400 km to 500 km.
 6. The constellation claimed in claim 2wherein said sight angle of one satellite relative to the nadir is from30° to 50° and is preferably about 45°.
 7. The constellation claimed inclaim 2 wherein said satellites of said constellation have differentangles between the projection of said sight axis on the surface of theEarth and the projection of the speed of said satellite on the Earth. 8.The constellation claimed in claim 7 including two satellites and inwhich the difference between said angles is from 75° to 105° and ispreferably about 90°.
 9. The constellation claimed in claim 8 includingthree satellites and in which the difference between said angles is from90° to 150° and is preferably about 120°.
 10. The constellation claimedin claim 1 wherein the tracks on the surface of the Earth of said sightaxes of said satellites of said constellation are substantiallycoincident in a first area of the surface of the Earth.
 11. Theconstellation claimed in claim 1 wherein the tracks on the surface ofthe Earth of the sight axes of said satellites of said constellation aresubstantially regularly distributed in a second area of the surface ofthe Earth.
 12. The constellation claimed in claim 1 when it satisfiesthe condition:${\frac{2\pi \quad T_{S}}{n\quad T}R} < {{\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}} - {\tan \quad \alpha_{i}\sin \quad \phi_{i}}}}} + {\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}}} \leq {a + {\frac{2\quad \pi \quad T_{S}}{n\quad T}R}}$

in which n is the number of satellites in the constellation, T is theperiod of rotation of the Earth, T_(S) is the orbital period, R is theradius of the Earth, H is the orbital altitude, γ is the angle betweenthe projection of the speed of satellite i on the surface of the Earthon passing over the equator and the rotation speed of the earth at theequator, ac is the angle between the sight axis of satellite i and thenadir, φ_(i) is the angle between the projection on the Earth of thesight axis of satellite i and the projection on the Earth of the speedof that satellite, ψ_(i,i+1) is the angle measured in the plane of theorbit between the satellites i and i+1, and a is a parameter analogousto a distance and is less than 500 km.
 13. The constellation claimed inclaim 12 wherein said parameter a has a value less than 100 km andpreferably less than 50 km.
 14. The constellation claimed in claim 1wherein the angle between two satellites of said constellation in theplane of said orbit satisfies the condition:${\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} \leq {\frac{H}{\cos \quad \gamma}{{{\tan \quad \alpha_{i}\sin \quad \phi_{i}} - {\tan \quad \alpha_{i + 1}\sin \quad \phi_{i + 1}}}}} \leq {{\frac{T_{S}}{T}R\quad \psi_{i,{i + 1}}} + b}$

in which T is the rotation period of the Earth, T_(S) is the orbitalperiod, H is the orbital altitude, γ is the angle between the projectionof the speed of satellite i on the surface of the Earth on crossing theequator and the rotation speed of the Earth at the equator, α_(i) is theangle between the sight axis of satellite i and the nadir, φ₁ is theangle between the projection of the sight axis of satellite i on theEarth and the projection of the speed of said satellite on the Earth,ψ_(i,i+1) is the angle measured in the plane of the orbit betweensatellites i and i+1, and b is a parameter analogous to a distance andis less than 200 km.
 15. The constellation claimed in claim 14 whereinsaid parameter b has a value less than 20 km and preferably less than 10km.